In the NIST/ASME Steam Properties database, Version 2.2, the equilibrium thermodynamic properties for water are calculated from the 1995 Formulation for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, issued by the International Association for the Properties of Water and Steam (IAPWS) [1,2].
The formulation consists of a fundamental equation for the Helmholtz energy per unit mass (kg), made dimensionless by RmT, (where Rm is a mass-based gas constant and T is the temperature), as a function of temperature and density. When combined with a function for the ideal gas Helmholtz energy [3], a complete Helmholtz energy surface is defined. All other thermodynamic properties can then be obtained by differentiation of this surface. Conditions of vapor-liquid equilibrium can be established by finding a pressure where, at the given temperature, the vapor and liquid densities produce not only that pressure, but also identical fugacities.
Some properties may be reported on either a mass or molar basis. The basic formulation is in terms of mass; conversion to moles is performed using a molar mass of 18.015268 g/mol. This molar mass corresponds to that of Vienna Standard Mean Ocean Water (VSMOW), which is an internationally recognized standard for the isotopic composition of water [4-7].
Some properties (such as isobaric heat capacity, isothermal compressibility, speed of sound, and Joule-Thomson coefficient) are not defined in the two-phase region. Therefore, calculations at a two-phase condition produce a result of “not applicable” for these properties.
All thermodynamic properties that can be computed by the database are listed below, with comments when needed for clarification. Definitions for most of these quantities may be found in [8].
Temperature
Temperatures are on the International Temperature Scale of 1990 [9].
Pressure
Density
Volume
Quality
For a two-phase condition,quality is defined as the amount of water in the vapor phase divided by the total amount of water. For the saturated liquid and saturated vapor, the quality is 0.0 and 1.0, respectively. One-phase fluids that are subcooled or uperheated are so designated. If the pressure is above the critical pressure (22.064 MPa), there is no rigorous definition of these terms; the database designates the fluid as “superheated” if the temperature is above the critical temperature and “subcooled” if it is below.
Enthalpy
The zero for the enthalpy function is determined by the conventions (see below) that the entropy and internal energy functions are zero for the saturated liquid at the triple point.
For the enthalpy and other quantities containing dimensions of energy, varying definitions are sometimes used for the non-SI units of calories and Btu’s. When those units are used in this database, the conversion to and/or from SI units is based on the International Table calorie, defined by the Fifth International Conference on the Properties of Steam to be exactly 4.1868 joules. The corresponding International Table Btu is approximately 1055.056 joules. These values differ slightly from other common definitions, such as the “thermochemical” calorie which is defined as 4.184 joules.
Entropy
The arbitrary zero for the entropy function is chosen to be the saturated liquid at the triple point. Together with the internal energy zero, this defines the scale for the enthalpy, Helmholtz energy, and Gibbs energy.
Isochoric Heat Capacity
The isochoric(constant-volume) heat capacity is defined by:
where u is the internal energy per unit mass.
For states within the two-phase region, this property exists (as opposed to the constant-pressure heat capacity, which is divergent), but requires a more complicated calculation than for the one-phase region. The basic equation is:
whereQis the quality,uv and ul are the internal energy of the saturated vapor and liquid, respectively, and Duvapis the internal energy change of vaporization. Subscripts sat and V indicate derivatives evaluated under the constraint of vapor-liquid saturation and at constant volume, respectively. Evaluation of the derivatives in the above equation makes use of other calculated quantities such as the heat capacities, densities and volume expansivities of the individual phases, and the slope of the vapor-pressure curve with respect to temperature.
Isobaric Heat Capacity
The isobaric (constant-pressure) heat capacity is defined by:
Internal Energy
The arbitrary zero for the internal energy function is chosen to be the saturated liquid at the triple point (273.16 K, 611.657 Pa).
Helmholtz Energy
Gibbs Energy
Fugacity
Isothermal Compressibility
This quantity, often written as kT, is defined by:
Volume Expansivity
This quantity, often written as a, is defined by:
Isothermal dp/dr
Isochoric dp/dT
Speed of Sound
Joule-Thomson Coefficient
This coefficient,often written as m, is defined by:
Additional Derivatives
The database can also calculate several additional derivatives of the equation of state. These are the second derivatives of pressure as a function of temperature and density, and the first and second derivatives of density as a function of temperature and pressure.
Calculations for both the viscosity and the thermal conductivity are based on formulations adopted by IAPWS (then IAPS) in 1985 [10]. Those formulations, however, are slightly outdated because they do not correspond to the 1990 temperature scale and because they make use of an isothermal compressibility computed from an obsolete water equation of state. In this revised implementation, adopted by IAPWS in 1997 (viscosity) and 1998 (thermal conductivity), we use the same equations with temperatures on the 1990 scale with the compressibility calculated from the 1995 IAPWS formulation for thermodynamic properties [1,2].
Surface Tension
The vapor-liquid surface tension is calculated according to the IAPWS 1994 formulation for the Surface Tension of Ordinary Water Substance [11]. Note that the table of surface tension values (Table 1) given in this reference is incorrect, but the surface tension formula is correct.
Dielectric Constant
The static dielectric constant (or relative permittivity, where the permittivity of a vacuum is defined to be unity) is correlated as a function of temperature and density [12]. This formulation contains a singularity at the temperature of 228 K; calculations at or below that temperature (which is only possible for vapors at extremely low pressures) return a value of “not applicable” for the dielectric constant.
The database also calculates several derivatives of the dielectric constant. These are the first derivative with respect to density at constant temperature, the first derivative with respect to temperature at constant density, and the first and second derivatives as a function of pressure and temperature.
Debye-Hückel SlopesThe so-called Debye-Hückel slopes are used by solution chemists to describe the contributions of electrostatic effects to the thermodynamic properties of ionic solutions. Definitions of these quantities may be found in [12]. This database computes the Debye-Hückel slopes for activity coefficient, osmotic coefficient, apparent molar volume, apparent molar enthalpy, apparent molar compressibility, and apparent molar heat capacity.
Refractive Index
The refractive index (relative to a vacuum) is computed as a function of temperature, density, and wavelength according to a formulation adopted by IAPWS [13]. This correlation is primarily intended for wavelengths in the visible region, but also extends somewhat into the ultraviolet and the near infrared.
Solid Phase Boundaries
This database does not compute any properties of the solid phases of water. However, it does give the conditions at which solid and fluid are in equilibrium. The database also gives the ice form in equilibrium with the fluid at a given condition. The vapor-solid and liquid-solid boundaries are given by the IAPWS 1993 formulation for the Pressure along the Melting and the Sublimation Curves of Ordinary Water Substance [14].
Uncertainties in Calculated Properties
The properties calculated by this database have associated uncertainties, arising from the precision and scatter of the underlying experimental data and from the fit of the formulation to those data. In general, information about these uncertainties may be found in the IAPWS release document for the property in question. However, since the thermodynamic properties are of interest to the most users and their uncertainties have been conveniently summarized in graphical form, we present here four figures, taken from the IAPWS release [1], which show the uncertainties for key thermodynamic properties as a function of pressure and temperature.
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Figure B-1. Estimated uncertainties in density. In the enlarged critical region (triangle), a percent uncertainty in pressure is given. This region is bordered by the two isochores 527 kg×m-3 and 144 kg×m-3 and by the 30 MPa isobar. The positions of the lines separating the uncertainty regions are approximate
Figure B-2. Estimated uncertainties in speed of sound. For the definition of the region around the critical point, see Figure B-1. The positions of the lines separating the uncertainty regions are approximate.
Figure B-3. Estimated uncertainties in isobaric heat capacity cp. For the definition of the region around the critical point, see Figure B-1. The positions of the lines separating the uncertainty regions are approximate.
Figure B-4. Estimated uncertainties in vapor pressure pQ, saturated liquid density p', and saturated vapor density p".
References
[1] Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. Copies of this and other IAPWS releases can be obtained from the Executive Secretary of IAPWS, Dr. R.B. Dooley, Electric Power Research Institute, 3412 Hillview Avenue, Palo Alto, CA 94304.
[2] W. Wagner and A. Pruss, "New International Formulation for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use," J. Phys. Chem. Ref. Data, submitted (2000).
[3] J.R. Cooper, “Representation of the Ideal-Gas Thermodynamic Properties of Water,” Int. J. Thermophysics, 3, 35 (1982).
[4] H. Craig, “Standard for Reporting Concentrations of Deuterium and Oxygen-18 in Natural Waters,” Science, 133, 1833 (1961).
[5] R. Gonfiantini, “Standards for stable isotope measurements in natural compounds,” Nature, 271, 534 (1978).
[6] T.B. Coplen, “Reporting of Stable Hydrogen, Carbon, and Oxygen Isotopic Abundances,” Pure Appl. Chem., 66, 273 (1994).
[7] Report of Investigation, NIST Standard Reference Material 8535 (Vienna Standard Mean Ocean Water), NIST Standard Reference Materials Program, Gaithersburg, Maryland, 1992.
[8] International Union of Pure and Applied Chemistry, Quantities, Units and Symbols in Physical Chemistry, second edition, Blackwell Science, Oxford (1993).
[9] H. Preston-Thomas, “The International Temperature Scale of 1990 (ITS-90),” Metrologia, 27, 3 (1990).
[10] J. Kestin, J.V. Sengers, B. Kamgar-Parsi, and J.M.H. Levelt Sengers, “Thermophysical Properties of Fluid H2O,” J. Phys. Chem. Ref. Data, 13, 175 (1984).
[11] IAPWS Release on The Surface Tension of Ordinary Water Substance, in H.J. White, J.V. Sengers, D.B. Neumann, and J.C. Bellows, eds., Physical Chemistry of Aqueous Systems, Proc. 12th Int. Conf. on the Properties of Water and Steam, A139 (1995).
[12] D.P. Fernandez, A.R.H. Goodwin, E.W. Lemmon, J.M.H. Levelt Sengers, and R.C. Williams, “A Formulation for the Static Permittivity of Water and Steam at Temperatures from 238 to 873 K at Pressures up to 1200 MPa, Including Derivatives and Debye-Hückel Coefficients,” J. Phys. Chem. Ref. Data, 26, 1125 (1997).
[13] A.H. Harvey, J.S. Gallagher, and J.M.H. Levelt Sengers, "Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density," J. Phys. Chem. Ref. Data, 27, 761 (1998).
[14] W. Wagner, A. Saul, and A. Pruss, “International Equations for the Pressure along the Melting and along the Sublimation Curve of Ordinary Water Substance,” J. Phys. Chem. Ref. Data, 23, 515 (1994).
